Linguistic Interpretation of Mathematical Morphology

Mathematical Morphology is a theory based on geometry, algebra, topology and set theory, with strong application to digital image processing. This theory is characterized by two basic operators: dilation and erosion. In this work we redefine these operators based on compensatory fuzzy logic using a linguistic definition, compatible with previous definitions of Fuzzy Mathematical Morphology. A comparison to previous definitions is presented, assessing robustness against noise.Fil: Bouchet, Agustina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Mar del Plata; ArgentinaFil: Meschino, Gustavo. Universidad Nacional de Mar del Plata; ArgentinaFil: Brun, Marcel. Universidad Nacional de Mar del Plata; ArgentinaFil: Espin Andrade, Rafael. Instituto Superior Politécnico José Antonio Echeverría Cujae; CubaFil: Ballarin, Virginia. Universidad Nacional de Mar del Plata; Argentin

Quasi-arithmetic means and OWA functions in interval-valued and Atanassov's intuitionistic fuzzy set theory

In this paper we propose an extension of the well-known OWA functions introduced by Yager to interval-valued (IVFS) and Atanassov’s intuitionistic (AIFS) fuzzy set theory. We first extend the arithmetic and the quasi-arithmetic mean using the arithmetic operators in IVFS and AIFS theory and investigate under which conditions these means are idempotent. Since on the unit interval the construction of the OWA function involves reordering the input values, we propose a way of transforming the input values in IVFS and AIFS theory to a new list of input values which are now ordered

Fuzzy Aggregators - an Overview

The article deals with mathematical formalism of the process of combining several inputs into a single output in fuzzy inteligent systems, the process known as aggregation. We are interested in logic aggregation operators. Such aggregators are present in most decision problems and in fuzzy expert systems. Fuzzy inteligent systems are equipped with aggregation operators (aggregators) with which reasoning models adapt well to human reasoning. A brief overview of the field of fuzzy aggregators is given. Attention is devoted to so called graded logic aggregators.. The role of fuzzy agregators in modelling reasoning and the way they are chosen in modelling are pointed out. The conclusions are given and research in the field is pointed out

Constraint-wish and satisfied-dissatisfied: an overview of two approaches for dealing with bipolar querying

In recent years, there has been an increasing interest in dealing with user preferences in flexible database querying, expressing both positive and negative information in a heterogeneous way. This is what is usually referred to as bipolar database querying. Different frameworks have been introduced to deal with such bipolarity. In this chapter, an overview of two approaches is given. The first approach is based on mandatory and desired requirements. Hereby the complement of a mandatory requirement can be considered as a specification of what is not desired at all. So, mandatory requirements indirectly contribute to negative information (expressing what the user does not want to retrieve), whereas desired requirements can be seen as positive information (expressing what the user prefers to retrieve). The second approach is directly based on positive requirements (expressing what the user wants to retrieve), and negative requirements (expressing what the user does not want to retrieve). Both approaches use pairs of satisfaction degrees as the underlying framework but have different semantics, and thus also different operators for criteria evaluation, ranking, aggregation, etc

IOWA & Cross-ratio Uninorm operators as aggregation tools in sentiment analysis and ensemble methods

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.In the field of Sentiment Analysis, a number of different classifiers are utilised to attempt to establish the polarity of a given sentence. As such, there could be a need for aggregating the outputs of the algorithms involved in the classification effort. If the output of every classification algorithm resembles the opinion of an expert in the subject at hand, we are then in the presence of a group decision making problem, which in turn translates into two sub-problems: (a) defining the desired semantic of the aggregation of all opinions, and (b) applying the proper aggregation technique that can achieve the desired semantic chosen in (a). The objective of this article is twofold. Firstly, we present two specific aggregation semantics, namely fuzzy-majority and compensatory, which are based on Induced Ordered Weighted Averaging and Uninorm operators, respectively. Secondly, we show the power of these two techniques by applying them to an existing hybrid method for classification of sentiments at the sentence level. In this case, the proposed aggregation solutions act as a complement in order to improve the performance of the aforementioned hybrid method. In more general terms, the proposed solutions could be used in the creation of semantic-sensitive ensemble methods, instead of the more simple ensemble choices available today in commercial machine learning software offerings

Managing Epistemic Uncertainty in Design Models through Type-2 Fuzzy Logic Multidisciplinary Optimization

Humans have a natural ability to operate in dynamic environments and perform complex tasks with little perceived effort. An experienced ship designer can intuitively understand the general consequences of design choices and the general attributes of a good vessel. A person's knowledge is often ill-structured, subjective, and imprecise, but still incredibly effective at capturing general patterns of the real-world or of a design space. Computers on the other hand, can rapidly perform a large number of precise computations using well-structured, objective mathematical models, providing detailed analyses and formal evaluations of a specfic set of design candidates. In ship design, which involves generating knowledge for decision-making through time, engineers interactively use their own mental models and information gathered from computer-based optimization tools to make decisions which steer a vessel's design. In recent decades, the belief that large synthesis codes can help achieve cutting-edge ship performance has led to an increased popularity of optimization methods, potentially leading to rewarding results. And while optimization has proven fruitful to structural engineering and the aerospace industry, its applicability to early-stage design is more limited for three main reasons. First, mathematical models are by definition a reduction which cannot properly describe all aspects of the ship design problem. Second, in multidisciplinary optimization, a low-fidelity model may incorrectly drive a design, biasing the system level solution. Finally, early-stage design is plagued with limited information, limiting the designer's ability to develop models to inform decisions. This research extends previously done work by incorporating type-2 fuzzy logic into a human-centric multidisciplinary optimization framework. The original framework used type-1 fuzzy logic to incorporate human expertise into optimization models through linguistic variables. However, a type-1 system does not properly account for the uncertainty associated with linguistic terms, and thus does not properly represent the uncertainty associated with a human mental model. This limitation is corrected with the type-2 fuzzy logic multidisciplinary optimization presented in this work, which more accurately models a designer's ability to "communicate, reason and make rational decisions in an environment of imprecision, uncertainty, incompleteness of information and partiality of truth" (Mendel et al., 2010). It uses fuzzy definitions of linguistic variables and rule banks to incorporate "human intelligence" into design models, and better handles the linguistic uncertainty inherent to human knowledge and communication. A general mathematical optimization proof of concept and a planing craft case study are presented in this dissertation to show how mathematical models can be enhanced by incorporating expert opinion into them. Additionally, the planing craft case study shows how human mental models can be leveraged to quickly estimate plausible values of ship parameters when no model exists, increasing the designer's ability to run optimization methods when information is limited.PHDNaval Architecture & Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145891/1/doriancb_1.pd

A Fuzzy Logic-Based Foundation for Analyzing Imprecise Conflicting Requirements

Imprecise requirements are represented by the canonical form in test-score semantics. The concepts of feasibility, satisfiability, and specificity are formalized based on the fuzzy sets. The relationships between requirements are classified to be conflicting and cooperative. A feasible overall requirement can thus be formulated based on the tradeoff analysis of the conflicting requirements by using fuzzy multi-criteria optimization techniqu

A fuzzy multiple attribute decision making tool for HVAC&R systems selection with considering the future probabilistic climate changes and electricity decarbonisation plans in the UK

Buildings account for 40% of total energy consumption in the UK and more than 55% of this energy is used by heating, ventilation, air-conditioning and refrigeration (HVAC&R) systems. This significant energy demand and the ascending trend in utilising HVAC&R systems together with the global need to impose energy-efficiency measures underline the importance of selecting the most appropriate HVAC&R system during the design process. This paper reviewed and classified a broad range of principal multiple attribute decision making methods. Among them, the fuzzy multiple attribute decision making approach was adopted to develop a decision making tool for HVAC&R systems selection. This was mainly due to the ability of this method to deal with the uncertainties and imprecisions of the linguistic terms involved in the decision making process. In order to make a decision on HVAC&R systems selection, 58 alternative systems, including both primary and secondary parts, were examined. The scope of this study enabled the consideration of all 18 climate regions in the UK and included the effects of climate change. In addition, the Government’s electricity decarbonisation plans were integrated within the developed decision making model for HVAC&R systems selection in office buildings in the UK. Finally, the model was transferred into a computational tool with a user-friendly interface